KABUL - With crowds again besieging Afghanistan's largest private bank after a day's respite for Friday prayer, Afghan authorities on Saturday grasped for a plan to shore up tottering Kabul Bank and avoid potential economic and political turmoil.

One option, according to a person familiar with discussions between President Hamid Karzai and key protagonists in the drama, is that the state take possession of a substantial part of the bank's shares. This would allow the government to inject money into a bank that, although entirely privately owned, plays a key role in the functioning of the state because it handles payments for soldiers, police and teachers.

In a sign of his determination to stabilize Kabul Bank, Karzai ordered Afghan police to take over guard duties at bank branches from a private security company, said Sherkhan Farnood, the bank's founder and ousted chairman.

Kabul Bank depositors on Saturday yanked out about $69 million, less than on Wednesday and Thursday. But this was largely because the bank ran out of cash at many branches when the Central Bank had trouble delivering funds. Kabul Bank began the week with $500 million in liquid assets, most of it stashed with the Central Bank, but now has less than half that amount.

Saturday's renewed stampede by depositors represented a blunt vote of no confidence in Karzai, who had assured Afghans that Kabul Bank would not collapse and accused Western news media of overstating its problems.

Some Kabul Bank shareholders, including Mahmoud Karzai, the president's brother, and Khalilullah Fruzi, the bank's former chief executive, have called on the United States to offer a bail out.

The U.S. Treasury Department has sent a team of experts to Kabul to help but has ruled out sending cash. "This is an Afghan issue. They are taking immediate steps to ensure the stability of Kabul Bank," said Deputy Treasury Secretary Neal Wolin. "No American taxpayer funds will be used to support Kabul Bank."

The Central Bank declined to comment on how authorities might salvage Kabul Bank.

At a meeting late Thursday at the Presidential Palace, Karzai, the Central Bank governor, the finance minister and others, including Fruzi and Farnood, discussed the possibility of the Central Bank taking a substantial stake in the bank. This would be achieved by ordering shareholders who have not paid for their shares to do so or transfer their rights to the Central Bank.

About 51 percent of Kabul Bank shares were acquired with loans from Kabul Bank. It is highly irregular for a bank to loan individuals money to buy shares in itself. The president's own brother, Mahmoud, became the bank's third-biggest shareholder in this way.

Kabul Bank, which has 1.4 million customers, is entangled in a skein of loans to its own shareholders and politically connected insiders, as well as property deals in Dubai.

Kabul Bank reopened Saturday with a long line of anxious customers outside the main branch in the capital by 8 a.m.

By late-morning, the bank had run out of U.S. dollars and had only Afghanis left. Around 60 percent of the bank's deposits are held in dollar accounts.

Farnood, the former Kabul Bank chairman and still a big shareholder, said the bank should be able to start paying depositors in full again Sunday, which is a business day in Afghanistan.

The crisis began after news broke Tuesday that the Central Bank, on orders from President Karzai, had purged Kabul Bank's top two executives. This prompted customers to flock to branches Wednesday and Thursday and pull out roughly $200 million.

While mostly businessmen appeared to be withdrawing cash Wednesday and Thursday, working-class residents seeking smaller amounts thronged the bank Saturday. One window dedicated to serving female customers was mobbed.

One named Nasima waited five hours to withdraw $2,200. "This bank has no future," she said.